Discrete cosine transform (DCT). 
Let us start with the one-dimensional type II discrete cosine transform (DCT) [1]} formulated as
\(D_1[\mathbf {x}](k) = \sqrt{\frac{2}{d}}(\frac{1}{\sqrt{2}}\cos \big (\frac{\pi }{d}\frac{k}{2}\big )\mathbf {x}(0)+\sum _{n=1}^{d-1}\cos (\frac{\pi }{d}(n+\frac{1}{2})k)\mathbf {x}(n)),k=0,\dots ,d-1,\) 
